superlet module

QhX.algorithms.superlets.superlet.FASLT(data_arr, samplerate, scales, order_max, order_min=1, c_1=3)[source]

Performs a Fractional Adaptive Superlet Transform (FASLT) on time-series data.

FASLT computes a time-frequency representation using a set of Morlet wavelets with fractional orders. The order of wavelets increases linearly with frequency, allowing for a more adaptive analysis across a range of frequencies.

Parameters:

  • data_arr (ndarray) – Time-series data for analysis.

  • samplerate (float) – Sampling rate of the data in Hz.

  • scales (ndarray) – Array of scales for the wavelet transform.

  • order_max (int) – Maximum order of the superlet set.

  • order_min (int, optional) – Minimum order of the superlet set, default is 1.

  • c_1 (int, optional) – Number of cycles for the base Morlet wavelet, default is 3.

Returns:

ndarray

Return type:

Result of the Fractional Adaptive Superlet Transform.

class QhX.algorithms.superlets.superlet.MorletSL(c_i=3, k_sd=5)[source]

Bases: object

time(t, s=1.0)[source]

Computes the complex Morlet wavelet at a given time and scale.

Parameters:

  • (float) (-t) –

  • (float (-s) –

  • optional) (Scale variable, default is 1.0.) –

Returns:

complex

Return type:

Value of the Morlet wavelet at the given time and scale.

QhX.algorithms.superlets.superlet.compute_adaptive_order(freq, order_min, order_max)[source]

Computes the superlet order for given frequencies in the Fractional Adaptive SLT.

This is a linear mapping between the minimal and maximal order onto the respective minimal and maximal frequencies.

Parameters:

  • (ndarray) (- freq) – Array of frequencies of interest.

  • (int) (- order_max) – Minimal order in the superlet set.

  • (int) – Maximal order in the superlet set.

Returns:

ndarray

Return type:

Array of computed orders for the given frequencies.

QhX.algorithms.superlets.superlet.cwtSL(data, wavelet, scales, dt)[source]

Performs Continuous Wavelet Transform using a specified wavelet and scales.

Parameters:

  • data (-) – Time-series data for analysis.

  • wavelet (-) – Morlet wavelet object used for the transform.

  • scales (-) – Array of scales for the wavelet transform.

  • dt (-) – Time step of the data.

Returns:

ndarray

Return type:

Continuous wavelet transform of the input data.

QhX.algorithms.superlets.superlet.fourier_period(scale)[source]

Calculates the approximate Fourier period for a given scale using Morlet wavelet.

Parameters:

(float) (-scale) –

Returns:

  • float

  • Approximate Fourier period corresponding to the given scale.

QhX.algorithms.superlets.superlet.gen_superlet_testdata(freqs=[20, 40, 60], cycles=11, fs=1000, eps=0)[source]

Generates test data for superlet analysis, consisting of harmonic superpositions.

This function creates a signal composed of multiple oscillations with specified frequencies. Each oscillation is a few-cycle harmonic with an optional addition of white noise. It is useful for demonstrating and testing superlet transform functionality.

Parameters:

  • float (- freqs (list of) – Frequencies of the oscillations to be included in the signal. Default is [20, 40, 60] Hz.

  • optional) – Frequencies of the oscillations to be included in the signal. Default is [20, 40, 60] Hz.

  • (int (- fs) – Number of cycles for each oscillation. Default is 11.

  • optional) – Number of cycles for each oscillation. Default is 11.

  • (int – Sampling frequency in Hz. Default is 1000 Hz.

  • optional) – Sampling frequency in Hz. Default is 1000 Hz.

  • (float (- eps) – Standard deviation of additive white noise. Default is 0 (no noise).

  • optional) – Standard deviation of additive white noise. Default is 0 (no noise).

Returns:

ndarray

Return type:

Generated 1D signal array containing harmonic superpositions with optional noise.

Examples

>>> import numpy as np
>>> from mymodule import gen_superlet_testdata
>>> signal = gen_superlet_testdata(freqs=[20, 40, 60], cycles=10, fs=1000, eps=0.1)
QhX.algorithms.superlets.superlet.multiplicativeSLT(data_arr, samplerate, scales, order_max, order_min=1, c_1=3)[source]

Performs a multiplicative Superlet Transform on time-series data.

This function computes the multiplicative Superlet Transform by combining Morlet wavelets with increasing cycles, resulting in a super-resolution time-frequency representation.

Parameters:

  • data_arr (ndarray) – Time-series data for analysis.

  • samplerate (float) – Sampling rate of the data in Hz.

  • scales (ndarray) – Array of scales for the wavelet transform.

  • order_max (int) – Maximum order of the superlet set.

  • order_min (int, optional) – Minimum order of the superlet set, default is 1.

  • c_1 (int, optional) – Number of cycles for the base Morlet wavelet, default is 3.

Returns:

ndarray

Return type:

Result of the multiplicative Superlet Transform.

QhX.algorithms.superlets.superlet.scale_from_period(period)[source]

Determines the scale corresponding to a given Fourier period using Morlet wavelet.

Parameters:

(float) (-period) –

Returns:

float

Return type:

Scale corresponding to the given Fourier period.

QhX.algorithms.superlets.superlet.superlet(data_arr, samplerate, scales, order_max, order_min=1, c_1=3, adaptive=False)[source]

Performs Superlet Transform (SLT) on time-series data.

This function computes either a multiplicative SLT or a fractional adaptive SLT (FASLT), based on the ‘adaptive’ flag. Multiplicative SLT is recommended for analysis within a narrow frequency band, while FASLT is suitable for a broader range of frequencies. The transform combines multiple Morlet wavelets with varying cycles to achieve super-resolution in time-frequency analysis.

Parameters:

  • data_arr (ndarray) – Uniformly sampled time-series data. The first dimension is treated as the time axis.

  • samplerate (float) – Sampling rate of the time-series data in Hz.

  • scales (ndarray) – Array of scales for the wavelet transform, ordered from high to low for adaptive=True.

  • order_max (int) – Maximum order for the superlet set, dictating the highest number of cycles.

  • order_min (int, optional) – Minimum order for the superlet set, default is 1.

  • c_1 (int, optional) – Base number of cycles for the lowest-order Morlet wavelet, default is 3.

  • adaptive (bool, optional) – Flag to choose between multiplicative SLT and FASLT, default is False.

Returns:

ndarray

Return type:

Geometric mean of the complex time-frequency representation of the input data.

References

This module provides a suite of functions for time-frequency analysis using superlet transforms. Functions include methods for generating test data, scaling from periods, performing the superlet transform, and other related utilities.